Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
824703 | International Journal of Engineering Science | 2016 | 8 Pages |
Analysis of the transformation of one data set into another is a ubiquitous problem in many fields of science. Many works approximate the transformation of a reference cluster of n vectors Xi (i = 1, 2,…,n) into another cluster of n vectors xi by a translation and a rotation using a least squares optimization to obtain the rotation tensor Q. The objective of this work is to prove that this rotation tensor Q exhibits unphysical dependence on the shape and orientation of the reference cluster. In contrast, when the transformation is approximated by a translation and a general non-singular tensor F, which includes deformations, then the associated rotation tensor R does not exhibit these unphysical properties. An example in biomechanics quantifies the errors of these unphysical properties.